2jyh-r7b3

Dataset statistics

Number of variables	17
Number of observations	896
Missing cells	1134
Missing cells (%)	7.4%
Duplicate rows	0
Duplicate rows (%)	0.0%
Total size in memory	268.9 KiB
Average record size in memory	307.3 B

Variable types

NUM	12
CAT	4
UNSUPPORTED	1

Warnings

`Category` has constant value "896"	Constant
`Year` has constant value "896"	Constant
`DBN` has a high cardinality: 216 distinct values	High cardinality
`Level 2#` is highly correlated with `Students Tested`	High correlation
`Students Tested` is highly correlated with `Level 2#`	High correlation
`Level 3 and 4#` is highly correlated with `Level 3#`	High correlation
`Level 3#` is highly correlated with `Level 3 and 4#`	High correlation
`Level 3 and 4%` is highly correlated with `Mean Scale Score` and 1 other fields	High correlation
`Mean Scale Score` is highly correlated with `Level 3 and 4%`	High correlation
`Level 3%` is highly correlated with `Level 3 and 4%`	High correlation
`NYC Results on the New York State 2006 Math Test (Grades 3-8)` has 896 (100.0%) missing values	Missing
`Mean Scale Score` has 218 (24.3%) missing values	Missing
`DBN` is uniformly distributed	Uniform
`NYC Results on the New York State 2006 Math Test (Grades 3-8)` is an unsupported type, check if it needs cleaning or further analysis	Unsupported
`Level 1#` has 19 (2.1%) zeros	Zeros
`Level 1%` has 19 (2.1%) zeros	Zeros
`Level 4#` has 75 (8.4%) zeros	Zeros
`Level 4%` has 75 (8.4%) zeros	Zeros

Reproduction

Analysis started	2020-12-12 21:53:30.692810
Analysis finished	2020-12-12 21:53:44.814962
Duration	14.12 seconds
Software version	pandas-profiling v2.9.0
Download configuration	config.yaml

NYC Results on the New York State 2006 Math Test (Grades 3-8)
Unsupported

MISSING
REJECTED
UNSUPPORTED

Missing	896
Missing (%)	100.0%
Memory size	7.1 KiB

DBN
Categorical

HIGH CARDINALITY
UNIFORM

Distinct	216
Distinct (%)	24.1%
Missing	0
Missing (%)	0.0%
Memory size	7.1 KiB

11X083	7
10X315	7
10X095	7
09X004	7
11X194	7
Other values (211)	861

Common Values
Overview

Value	Count	Frequency (%)
11X083	7	0.8%
10X315	7	0.8%
10X095	7	0.8%
09X004	7	0.8%
11X194	7	0.8%
12X211	7	0.8%
11X089	7	0.8%
10X015	7	0.8%
12X214	7	0.8%
10X003	7	0.8%
10X279	7	0.8%
11X175	7	0.8%
11X019	7	0.8%
10X020	7	0.8%
10X037	7	0.8%
09X218	7	0.8%
12X212	7	0.8%
07X029	6	0.7%
10X280	6	0.7%
07X025	6	0.7%
07X031	6	0.7%
10X306	6	0.7%
08X071	5	0.6%
12X134	5	0.6%
08X093	5	0.6%
Other values (191)	732	81.7%

Frequencies of value counts

Unique

Unique	0 ?
Unique (%)	0.0%

Histogram of lengths of the category

Length

Max length	6
Median length	6
Mean length	6
Min length	6

Overview of Unicode Properties

Unique unicode characters	11
Unique unicode categories	2 ?
Unique unicode scripts	2 ?
Unique unicode blocks	1 ?

The Unicode Standard assigns character properties to each code point, which can be used to analyse textual variables.

Most occurring characters

Value	Count	Frequency (%)
0	1213	22.6%
1	1123	20.9%
X	896	16.7%
2	487	9.1%
9	366	6.8%
3	275	5.1%
8	259	4.8%
7	240	4.5%
5	187	3.5%
4	167	3.1%
6	163	3.0%

Most occurring categories

Value	Count	Frequency (%)
Decimal Number	4480	83.3%
Uppercase Letter	896	16.7%

Most frequent Decimal Number characters

Value	Count	Frequency (%)
0	1213	27.1%
1	1123	25.1%
2	487	10.9%
9	366	8.2%
3	275	6.1%
8	259	5.8%
7	240	5.4%
5	187	4.2%
4	167	3.7%
6	163	3.6%

Most frequent Uppercase Letter characters

Value	Count	Frequency (%)
X	896	100.0%

Most occurring scripts

Value	Count	Frequency (%)
Common	4480	83.3%
Latin	896	16.7%

Most frequent Common characters

Value	Count	Frequency (%)
0	1213	27.1%
1	1123	25.1%
2	487	10.9%
9	366	8.2%
3	275	6.1%
8	259	5.8%
7	240	5.4%
5	187	4.2%
4	167	3.7%
6	163	3.6%

Most frequent Latin characters

Value	Count	Frequency (%)
X	896	100.0%

Most occurring blocks

Value	Count	Frequency (%)
ASCII	5376	100.0%

Most frequent ASCII characters

Value	Count	Frequency (%)
0	1213	22.6%
1	1123	20.9%
X	896	16.7%
2	487	9.1%
9	366	6.8%
3	275	5.1%
8	259	4.8%
7	240	4.5%
5	187	3.5%
4	167	3.1%
6	163	3.0%

Grade
Categorical

Distinct	7
Distinct (%)	0.8%
Missing	0
Missing (%)	0.0%
Memory size	7.1 KiB

All Grades	216
3	140
4	139
5	132
6	110
Other values (2)	159

Value	Count	Frequency (%)
All Grades	216	24.1%
3	140	15.6%
4	139	15.5%
5	132	14.7%
6	110	12.3%
7	88	9.8%
8	71	7.9%

Frequencies of value counts

Unique

Unique	0 ?
Unique (%)	0.0%

Histogram of lengths of the category

Length

Max length	10
Median length	1
Mean length	3.169642857
Min length	1

Overview of Unicode Properties

Unique unicode characters	15
Unique unicode categories	4 ?
Unique unicode scripts	2 ?
Unique unicode blocks	1 ?

The Unicode Standard assigns character properties to each code point, which can be used to analyse textual variables.

Most occurring characters

Value	Count	Frequency (%)
l	432	15.2%
A	216	7.6%
	216	7.6%
G	216	7.6%
r	216	7.6%
a	216	7.6%
d	216	7.6%
e	216	7.6%
s	216	7.6%
3	140	4.9%
4	139	4.9%
5	132	4.6%
6	110	3.9%
7	88	3.1%
8	71	2.5%

Most occurring categories

Value	Count	Frequency (%)
Lowercase Letter	1512	53.2%
Decimal Number	680	23.9%
Uppercase Letter	432	15.2%
Space Separator	216	7.6%

Most frequent Decimal Number characters

Value	Count	Frequency (%)
3	140	20.6%
4	139	20.4%
5	132	19.4%
6	110	16.2%
7	88	12.9%
8	71	10.4%

Most frequent Uppercase Letter characters

Value	Count	Frequency (%)
A	216	50.0%
G	216	50.0%

Most frequent Lowercase Letter characters

Value	Count	Frequency (%)
l	432	28.6%
r	216	14.3%
a	216	14.3%
d	216	14.3%
e	216	14.3%
s	216	14.3%

Most frequent Space Separator characters

Value	Count	Frequency (%)
	216	100.0%

Most occurring scripts

Value	Count	Frequency (%)
Latin	1944	68.5%
Common	896	31.5%

Most frequent Common characters

Value	Count	Frequency (%)
	216	24.1%
3	140	15.6%
4	139	15.5%
5	132	14.7%
6	110	12.3%
7	88	9.8%
8	71	7.9%

Most frequent Latin characters

Value	Count	Frequency (%)
l	432	22.2%
A	216	11.1%
G	216	11.1%
r	216	11.1%
a	216	11.1%
d	216	11.1%
e	216	11.1%
s	216	11.1%

Most occurring blocks

Value	Count	Frequency (%)
ASCII	2840	100.0%

Most frequent ASCII characters

Value	Count	Frequency (%)
l	432	15.2%
A	216	7.6%
	216	7.6%
G	216	7.6%
r	216	7.6%
a	216	7.6%
d	216	7.6%
e	216	7.6%
s	216	7.6%
3	140	4.9%
4	139	4.9%
5	132	4.6%
6	110	3.9%
7	88	3.1%
8	71	2.5%

Category
Categorical

CONSTANT
REJECTED

Distinct	1
Distinct (%)	0.1%
Missing	0
Missing (%)	0.0%
Memory size	7.1 KiB

All Students	896

Value	Count	Frequency (%)
All Students	896	100.0%

Frequencies of value counts

Unique

Unique	0 ?
Unique (%)	0.0%

Histogram of lengths of the category

Length

Max length	12
Median length	12
Mean length	12
Min length	12

Overview of Unicode Properties

Unique unicode characters	10
Unique unicode categories	3 ?
Unique unicode scripts	2 ?
Unique unicode blocks	1 ?

The Unicode Standard assigns character properties to each code point, which can be used to analyse textual variables.

Most occurring characters

Value	Count	Frequency (%)
l	1792	16.7%
t	1792	16.7%
A	896	8.3%
	896	8.3%
S	896	8.3%
u	896	8.3%
d	896	8.3%
e	896	8.3%
n	896	8.3%
s	896	8.3%

Most occurring categories

Value	Count	Frequency (%)
Lowercase Letter	8064	75.0%
Uppercase Letter	1792	16.7%
Space Separator	896	8.3%

Most frequent Uppercase Letter characters

Value	Count	Frequency (%)
A	896	50.0%
S	896	50.0%

Most frequent Lowercase Letter characters

Value	Count	Frequency (%)
l	1792	22.2%
t	1792	22.2%
u	896	11.1%
d	896	11.1%
e	896	11.1%
n	896	11.1%
s	896	11.1%

Most frequent Space Separator characters

Value	Count	Frequency (%)
	896	100.0%

Most occurring scripts

Value	Count	Frequency (%)
Latin	9856	91.7%
Common	896	8.3%

Most frequent Latin characters

Value	Count	Frequency (%)
l	1792	18.2%
t	1792	18.2%
A	896	9.1%
S	896	9.1%
u	896	9.1%
d	896	9.1%
e	896	9.1%
n	896	9.1%
s	896	9.1%

Most frequent Common characters

Value	Count	Frequency (%)
	896	100.0%

Most occurring blocks

Value	Count	Frequency (%)
ASCII	10752	100.0%

Most frequent ASCII characters

Value	Count	Frequency (%)
l	1792	16.7%
t	1792	16.7%
A	896	8.3%
	896	8.3%
S	896	8.3%
u	896	8.3%
d	896	8.3%
e	896	8.3%
n	896	8.3%
s	896	8.3%

Year
Categorical

CONSTANT
REJECTED

Distinct	1
Distinct (%)	0.1%
Missing	0
Missing (%)	0.0%
Memory size	7.1 KiB

2006	896

Value	Count	Frequency (%)
2006	896	100.0%

Frequencies of value counts

Unique

Unique	0 ?
Unique (%)	0.0%

Histogram of lengths of the category

Length

Max length	4
Median length	4
Mean length	4
Min length	4

Overview of Unicode Properties

Unique unicode characters	3
Unique unicode categories	1 ?
Unique unicode scripts	1 ?
Unique unicode blocks	1 ?

The Unicode Standard assigns character properties to each code point, which can be used to analyse textual variables.

Most occurring characters

Value	Count	Frequency (%)
0	1792	50.0%
2	896	25.0%
6	896	25.0%

Most occurring categories

Value	Count	Frequency (%)
Decimal Number	3584	100.0%

Most frequent Decimal Number characters

Value	Count	Frequency (%)
0	1792	50.0%
2	896	25.0%
6	896	25.0%

Most occurring scripts

Value	Count	Frequency (%)
Common	3584	100.0%

Most frequent Common characters

Value	Count	Frequency (%)
0	1792	50.0%
2	896	25.0%
6	896	25.0%

Most occurring blocks

Value	Count	Frequency (%)
ASCII	3584	100.0%

Most frequent ASCII characters

Value	Count	Frequency (%)
0	1792	50.0%
2	896	25.0%
6	896	25.0%

Mean Scale Score
Real number (ℝ_≥0)

HIGH CORRELATION
MISSING

Distinct	96
Distinct (%)	14.2%
Missing	218
Missing (%)	24.3%
Infinite	0
Infinite (%)	0.0%

Mean	648.1445428
Minimum	593
Maximum	699
Zeros	0
Zeros (%)	0.0%
Memory size	7.1 KiB

Quantile statistics

Minimum	593
5-th percentile	615.85
Q1	636
median	648
Q3	660
95-th percentile	681
Maximum	699
Range	106
Interquartile range (IQR)	24

Descriptive statistics

Standard deviation	18.79485122
Coefficient of variation (CV)	0.02899793176
Kurtosis	-0.02096183613
Mean	648.1445428
Median Absolute Deviation (MAD)	12
Skewness	-0.03173929843
Sum	439442
Variance	353.2464325
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
655	22	2.5%
647	19	2.1%
641	19	2.1%
653	19	2.1%
656	19	2.1%
651	18	2.0%
645	18	2.0%
633	16	1.8%
636	16	1.8%
657	15	1.7%
650	14	1.6%
640	14	1.6%
637	13	1.5%
644	13	1.5%
646	13	1.5%
643	13	1.5%
649	12	1.3%
660	12	1.3%
661	12	1.3%
654	12	1.3%
642	12	1.3%
662	12	1.3%
658	12	1.3%
648	12	1.3%
664	12	1.3%
Other values (71)	309	34.5%
(Missing)	218	24.3%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
593	1	0.1%
597	2	0.2%
598	1	0.1%
601	1	0.1%
603	1	0.1%
604	1	0.1%
605	1	0.1%
606	1	0.1%
607	2	0.2%
608	2	0.2%

Value	Count	Frequency (%)
699	1	0.1%
696	1	0.1%
695	2	0.2%
694	1	0.1%
693	2	0.2%
690	3	0.3%
688	1	0.1%
687	7	0.8%
686	2	0.2%
685	2	0.2%

Students Tested
Real number (ℝ_≥0)

HIGH CORRELATION

Distinct	370
Distinct (%)	41.3%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	200.3169643
Minimum	1
Maximum	1316
Zeros	0
Zeros (%)	0.0%
Memory size	7.1 KiB

Quantile statistics

Minimum	1
5-th percentile	51
Q1	88
median	137
Q3	238.25
95-th percentile	561.5
Maximum	1316
Range	1315
Interquartile range (IQR)	150.25

Descriptive statistics

Standard deviation	189.396914
Coefficient of variation (CV)	0.9454861434
Kurtosis	9.062007247
Mean	200.3169643
Median Absolute Deviation (MAD)	59
Skewness	2.702765249
Sum	179484
Variance	35871.19104
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
88	10	1.1%
77	10	1.1%
83	8	0.9%
94	8	0.9%
89	8	0.9%
87	8	0.9%
64	8	0.9%
124	7	0.8%
127	7	0.8%
71	7	0.8%
66	7	0.8%
100	7	0.8%
153	7	0.8%
115	7	0.8%
112	7	0.8%
129	7	0.8%
157	7	0.8%
86	7	0.8%
96	7	0.8%
108	7	0.8%
114	6	0.7%
57	6	0.7%
109	6	0.7%
78	6	0.7%
106	6	0.7%
Other values (345)	715	79.8%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
1	1	0.1%
2	1	0.1%
16	2	0.2%
18	1	0.1%
19	1	0.1%
23	2	0.2%
24	2	0.2%
25	2	0.2%
28	2	0.2%
31	1	0.1%

Value	Count	Frequency (%)
1316	1	0.1%
1302	1	0.1%
1224	1	0.1%
1186	1	0.1%
1141	1	0.1%
1138	1	0.1%
1094	1	0.1%
1069	1	0.1%
1056	1	0.1%
1051	1	0.1%

Level 1#
Real number (ℝ_≥0)

ZEROS

Distinct	159
Distinct (%)	17.8%
Missing	2
Missing (%)	0.2%
Infinite	0
Infinite (%)	0.0%

Mean	40.95302013
Minimum	0
Maximum	418
Zeros	19
Zeros (%)	2.1%
Memory size	7.1 KiB

Quantile statistics

Minimum	0
5-th percentile	2
Q1	11
median	22
Q3	47
95-th percentile	141.35
Maximum	418
Range	418
Interquartile range (IQR)	36

Descriptive statistics

Standard deviation	53.82338114
Coefficient of variation (CV)	1.314271352
Kurtosis	13.16439458
Mean	40.95302013
Median Absolute Deviation (MAD)	14
Skewness	3.193702023
Sum	36612
Variance	2896.956357
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
12	28	3.1%
9	27	3.0%
11	26	2.9%
8	24	2.7%
16	23	2.6%
2	22	2.5%
14	21	2.3%
22	21	2.3%
17	19	2.1%
15	19	2.1%
18	19	2.1%
0	19	2.1%
25	19	2.1%
13	18	2.0%
7	18	2.0%
10	18	2.0%
20	18	2.0%
23	17	1.9%
3	17	1.9%
21	16	1.8%
6	16	1.8%
1	16	1.8%
28	16	1.8%
5	16	1.8%
19	14	1.6%
Other values (134)	407	45.4%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0	19	2.1%
1	16	1.8%
2	22	2.5%
3	17	1.9%
4	13	1.5%
5	16	1.8%
6	16	1.8%
7	18	2.0%
8	24	2.7%
9	27	3.0%

Value	Count	Frequency (%)
418	1	0.1%
391	1	0.1%
380	1	0.1%
370	1	0.1%
350	1	0.1%
320	1	0.1%
312	1	0.1%
293	1	0.1%
283	1	0.1%
281	1	0.1%

Level 1%
Real number (ℝ_≥0)

ZEROS

Distinct	356
Distinct (%)	39.8%
Missing	2
Missing (%)	0.2%
Infinite	0
Infinite (%)	0.0%

Mean	18.54317673
Minimum	0
Maximum	67.5
Zeros	19
Zeros (%)	2.1%
Memory size	7.1 KiB

Quantile statistics

Minimum	0
5-th percentile	2.6
Q1	10.2
median	16.8
Q3	24.1
95-th percentile	43.205
Maximum	67.5
Range	67.5
Interquartile range (IQR)	13.9

Descriptive statistics

Standard deviation	11.98403162
Coefficient of variation (CV)	0.6462771612
Kurtosis	1.4415262
Mean	18.54317673
Median Absolute Deviation (MAD)	6.85
Skewness	1.09321953
Sum	16577.6
Variance	143.6170139
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
0	19	2.1%
9.8	11	1.2%
20	9	1.0%
9.4	8	0.9%
18.3	8	0.9%
15.6	8	0.9%
17.5	7	0.8%
21.2	7	0.8%
14.9	6	0.7%
16.9	6	0.7%
11.4	6	0.7%
18	6	0.7%
17	6	0.7%
20.5	6	0.7%
20.2	6	0.7%
25	6	0.7%
19	6	0.7%
16.7	6	0.7%
19.4	6	0.7%
18.4	6	0.7%
11.3	6	0.7%
14.7	6	0.7%
7	5	0.6%
2.6	5	0.6%
3.6	5	0.6%
Other values (331)	718	80.1%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0	19	2.1%
0.3	1	0.1%
0.6	2	0.2%
1	1	0.1%
1.1	2	0.2%
1.3	1	0.1%
1.4	3	0.3%
1.7	1	0.1%
1.8	3	0.3%
1.9	1	0.1%

Value	Count	Frequency (%)
67.5	1	0.1%
66.1	1	0.1%
61.1	1	0.1%
58.9	1	0.1%
57.9	1	0.1%
57.8	1	0.1%
57.1	1	0.1%
56.2	1	0.1%
56.1	1	0.1%
55	1	0.1%

Level 2#
Real number (ℝ_≥0)

HIGH CORRELATION

Distinct	203
Distinct (%)	22.7%
Missing	2
Missing (%)	0.2%
Infinite	0
Infinite (%)	0.0%

Mean	65.12304251
Minimum	1
Maximum	553
Zeros	0
Zeros (%)	0.0%
Memory size	7.1 KiB

Quantile statistics

Minimum	1
5-th percentile	8
Q1	24
median	40
Q3	78
95-th percentile	209
Maximum	553
Range	552
Interquartile range (IQR)	54

Descriptive statistics

Standard deviation	73.11835552
Coefficient of variation (CV)	1.122772412
Kurtosis	12.30230511
Mean	65.12304251
Median Absolute Deviation (MAD)	21
Skewness	3.071253461
Sum	58220
Variance	5346.293914
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
21	28	3.1%
30	19	2.1%
22	18	2.0%
23	17	1.9%
34	17	1.9%
32	17	1.9%
26	16	1.8%
25	16	1.8%
31	15	1.7%
33	15	1.7%
36	14	1.6%
29	14	1.6%
40	14	1.6%
16	13	1.5%
38	13	1.5%
56	13	1.5%
18	12	1.3%
28	12	1.3%
20	12	1.3%
10	12	1.3%
15	12	1.3%
19	12	1.3%
39	12	1.3%
7	11	1.2%
35	11	1.2%
Other values (178)	529	59.0%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
1	4	0.4%
2	1	0.1%
3	4	0.4%
4	9	1.0%
5	6	0.7%
6	3	0.3%
7	11	1.2%
8	8	0.9%
9	8	0.9%
10	12	1.3%

Value	Count	Frequency (%)
553	1	0.1%
518	1	0.1%
506	1	0.1%
504	1	0.1%
496	1	0.1%
471	1	0.1%
469	1	0.1%
430	1	0.1%
410	1	0.1%
361	1	0.1%

Level 2%
Real number (ℝ_≥0)

Distinct	385
Distinct (%)	43.1%
Missing	2
Missing (%)	0.2%
Infinite	0
Infinite (%)	0.0%

Mean	30.98702461
Minimum	2.1
Maximum	68.9
Zeros	0
Zeros (%)	0.0%
Memory size	7.1 KiB

Quantile statistics

Minimum	2.1
5-th percentile	10.295
Q1	23.225
median	31.4
Q3	39.4
95-th percentile	48.8
Maximum	68.9
Range	66.8
Interquartile range (IQR)	16.175

Descriptive statistics

Standard deviation	11.39779204
Coefficient of variation (CV)	0.3678246682
Kurtosis	-0.3195785394
Mean	30.98702461
Median Absolute Deviation (MAD)	8.05
Skewness	-0.166957306
Sum	27702.4
Variance	129.9096635
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
33.3	10	1.1%
28.6	10	1.1%
36	8	0.9%
31	7	0.8%
37.1	7	0.8%
37.2	7	0.8%
32.2	6	0.7%
20	6	0.7%
35.5	6	0.7%
36.8	6	0.7%
42.1	6	0.7%
26.1	6	0.7%
24.6	6	0.7%
40	6	0.7%
39.8	6	0.7%
37.4	6	0.7%
26	6	0.7%
25	6	0.7%
31.3	6	0.7%
20.8	5	0.6%
27.9	5	0.6%
21.7	5	0.6%
29.8	5	0.6%
28.7	5	0.6%
14.9	5	0.6%
Other values (360)	737	82.3%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
2.1	1	0.1%
2.3	1	0.1%
2.8	1	0.1%
3.6	1	0.1%
4.2	1	0.1%
4.3	3	0.3%
4.8	2	0.2%
5.6	1	0.1%
5.7	3	0.3%
5.9	1	0.1%

Value	Count	Frequency (%)
68.9	1	0.1%
59.8	1	0.1%
57.4	1	0.1%
56.9	1	0.1%
56.6	2	0.2%
56	1	0.1%
55.8	1	0.1%
55.5	1	0.1%
55.1	1	0.1%
54.5	1	0.1%

Level 3#
Real number (ℝ_≥0)

HIGH CORRELATION

Distinct	221
Distinct (%)	24.7%
Missing	2
Missing (%)	0.2%
Infinite	0
Infinite (%)	0.0%

Mean	79.14653244
Minimum	0
Maximum	559
Zeros	1
Zeros (%)	0.1%
Memory size	7.1 KiB

Quantile statistics

Minimum	0
5-th percentile	16
Q1	35
median	55
Q3	94.75
95-th percentile	221.35
Maximum	559
Range	559
Interquartile range (IQR)	59.75

Descriptive statistics

Standard deviation	74.61083659
Coefficient of variation (CV)	0.9426924249
Kurtosis	9.278584537
Mean	79.14653244
Median Absolute Deviation (MAD)	25
Skewness	2.671714058
Sum	70757
Variance	5566.776936
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
41	17	1.9%
34	17	1.9%
38	17	1.9%
44	17	1.9%
37	15	1.7%
30	15	1.7%
35	14	1.6%
27	14	1.6%
29	13	1.5%
23	13	1.5%
46	12	1.3%
42	12	1.3%
32	12	1.3%
52	12	1.3%
45	12	1.3%
47	12	1.3%
89	11	1.2%
36	11	1.2%
51	11	1.2%
26	11	1.2%
25	10	1.1%
28	10	1.1%
78	10	1.1%
50	10	1.1%
49	10	1.1%
Other values (196)	576	64.3%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0	1	0.1%
1	1	0.1%
5	2	0.2%
6	2	0.2%
7	5	0.6%
8	2	0.2%
9	2	0.2%
10	3	0.3%
11	5	0.6%
12	6	0.7%

Value	Count	Frequency (%)
559	1	0.1%
507	1	0.1%
502	1	0.1%
482	1	0.1%
464	1	0.1%
440	1	0.1%
436	1	0.1%
430	1	0.1%
424	1	0.1%
389	1	0.1%

Level 3%
Real number (ℝ_≥0)

HIGH CORRELATION

Distinct	433
Distinct (%)	48.4%
Missing	2
Missing (%)	0.2%
Infinite	0
Infinite (%)	0.0%

Mean	41.91957494
Minimum	0
Maximum	81.1
Zeros	1
Zeros (%)	0.1%
Memory size	7.1 KiB

Quantile statistics

Minimum	0
5-th percentile	14.365
Q1	32.6
median	44
Q3	52.3
95-th percentile	62.505
Maximum	81.1
Range	81.1
Interquartile range (IQR)	19.7

Descriptive statistics

Standard deviation	14.3286019
Coefficient of variation (CV)	0.3418117174
Kurtosis	-0.1967819867
Mean	41.91957494
Median Absolute Deviation (MAD)	9.55
Skewness	-0.4473878889
Sum	37476.1
Variance	205.3088325
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
50	10	1.1%
53.7	9	1.0%
56.3	8	0.9%
43.6	7	0.8%
42.9	6	0.7%
46.3	6	0.7%
50.6	6	0.7%
35.2	6	0.7%
49.5	6	0.7%
48.5	6	0.7%
33.3	6	0.7%
48.9	6	0.7%
41.7	6	0.7%
40	6	0.7%
45.5	6	0.7%
40.6	5	0.6%
41.5	5	0.6%
42.6	5	0.6%
45.8	5	0.6%
52.5	5	0.6%
46.9	5	0.6%
42.7	5	0.6%
47.8	5	0.6%
45.9	5	0.6%
41	5	0.6%
Other values (408)	744	83.0%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0	1	0.1%
0.9	1	0.1%
5	1	0.1%
6.1	1	0.1%
6.5	1	0.1%
6.9	3	0.3%
7.3	2	0.2%
7.4	1	0.1%
8.4	1	0.1%
8.9	1	0.1%

Value	Count	Frequency (%)
81.1	1	0.1%
77.1	1	0.1%
75.8	1	0.1%
74	1	0.1%
73.6	1	0.1%
73.2	1	0.1%
73.1	1	0.1%
73	1	0.1%
72.3	1	0.1%
71.7	1	0.1%

Level 4#
Real number (ℝ_≥0)

ZEROS

Distinct	91
Distinct (%)	10.2%
Missing	2
Missing (%)	0.2%
Infinite	0
Infinite (%)	0.0%

Mean	15.53914989
Minimum	0
Maximum	133
Zeros	75
Zeros (%)	8.4%
Memory size	7.1 KiB

Quantile statistics

Minimum	0
5-th percentile	0
Q1	3
median	9
Q3	20
95-th percentile	56
Maximum	133
Range	133
Interquartile range (IQR)	17

Descriptive statistics

Standard deviation	20.07433358
Coefficient of variation (CV)	1.291855328
Kurtosis	8.305410535
Mean	15.53914989
Median Absolute Deviation (MAD)	7
Skewness	2.589522562
Sum	13892
Variance	402.9788687
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
0	75	8.4%
1	69	7.7%
2	55	6.1%
5	54	6.0%
4	51	5.7%
3	48	5.4%
10	36	4.0%
7	32	3.6%
9	31	3.5%
6	30	3.3%
8	29	3.2%
12	29	3.2%
11	23	2.6%
14	18	2.0%
20	18	2.0%
19	17	1.9%
21	16	1.8%
15	13	1.5%
24	13	1.5%
18	13	1.5%
13	12	1.3%
23	11	1.2%
17	11	1.2%
27	11	1.2%
26	10	1.1%
Other values (66)	169	18.9%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0	75	8.4%
1	69	7.7%
2	55	6.1%
3	48	5.4%
4	51	5.7%
5	54	6.0%
6	30	3.3%
7	32	3.6%
8	29	3.2%
9	31	3.5%

Value	Count	Frequency (%)
133	1	0.1%
131	1	0.1%
129	1	0.1%
119	1	0.1%
112	1	0.1%
111	1	0.1%
107	1	0.1%
104	1	0.1%
101	1	0.1%
100	2	0.2%

Level 4%
Real number (ℝ_≥0)

ZEROS

Distinct	252
Distinct (%)	28.2%
Missing	2
Missing (%)	0.2%
Infinite	0
Infinite (%)	0.0%

Mean	8.553579418
Minimum	0
Maximum	47.5
Zeros	75
Zeros (%)	8.4%
Memory size	7.1 KiB

Quantile statistics

Minimum	0
5-th percentile	0
Q1	2.3
median	6.3
Q3	11.6
95-th percentile	26.435
Maximum	47.5
Range	47.5
Interquartile range (IQR)	9.3

Descriptive statistics

Standard deviation	8.486097157
Coefficient of variation (CV)	0.9921106407
Kurtosis	3.105645449
Mean	8.553579418
Median Absolute Deviation (MAD)	4.4
Skewness	1.654015435
Sum	7646.9
Variance	72.01384496
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
0	75	8.4%
1.2	13	1.5%
1.4	13	1.5%
1.9	12	1.3%
0.8	12	1.3%
8.3	11	1.2%
2.9	11	1.2%
6.5	11	1.2%
9.8	11	1.2%
5.3	10	1.1%
3.4	10	1.1%
1.1	10	1.1%
1	10	1.1%
4	9	1.0%
6	9	1.0%
0.6	8	0.9%
2.3	8	0.9%
5.4	8	0.9%
2.7	8	0.9%
0.7	8	0.9%
4.5	8	0.9%
11.4	8	0.9%
7.7	8	0.9%
0.4	8	0.9%
6.3	7	0.8%
Other values (227)	588	65.6%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0	75	8.4%
0.1	1	0.1%
0.2	2	0.2%
0.3	2	0.2%
0.4	8	0.9%
0.5	5	0.6%
0.6	8	0.9%
0.7	8	0.9%
0.8	12	1.3%
0.9	5	0.6%

Value	Count	Frequency (%)
47.5	1	0.1%
45.8	1	0.1%
45.7	1	0.1%
44.2	1	0.1%
43.3	1	0.1%
42.2	1	0.1%
40.4	1	0.1%
39.8	1	0.1%
39.3	1	0.1%
38.6	1	0.1%

Level 3 and 4#
Real number (ℝ_≥0)

HIGH CORRELATION

Distinct	251
Distinct (%)	28.1%
Missing	2
Missing (%)	0.2%
Infinite	0
Infinite (%)	0.0%

Mean	94.68568233
Minimum	0
Maximum	688
Zeros	1
Zeros (%)	0.1%
Memory size	7.1 KiB

Quantile statistics

Minimum	0
5-th percentile	18
Q1	39.25
median	67
Q3	116
95-th percentile	267.35
Maximum	688
Range	688
Interquartile range (IQR)	76.75

Descriptive statistics

Standard deviation	90.77084765
Coefficient of variation (CV)	0.9586544176
Kurtosis	8.518029656
Mean	94.68568233
Median Absolute Deviation (MAD)	33
Skewness	2.579506578
Sum	84649
Variance	8239.346782
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
38	16	1.8%
37	13	1.5%
41	13	1.5%
52	13	1.5%
76	12	1.3%
31	12	1.3%
39	11	1.2%
43	11	1.2%
28	11	1.2%
49	11	1.2%
42	11	1.2%
60	11	1.2%
27	10	1.1%
46	10	1.1%
40	10	1.1%
80	10	1.1%
50	10	1.1%
67	9	1.0%
45	9	1.0%
32	9	1.0%
61	9	1.0%
44	9	1.0%
34	9	1.0%
47	8	0.9%
48	8	0.9%
Other values (226)	629	70.2%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0	1	0.1%
1	1	0.1%
5	1	0.1%
6	2	0.2%
7	6	0.7%
8	2	0.2%
9	1	0.1%
10	1	0.1%
11	6	0.7%
12	5	0.6%

Value	Count	Frequency (%)
688	1	0.1%
598	1	0.1%
554	1	0.1%
552	1	0.1%
541	1	0.1%
524	1	0.1%
521	1	0.1%
520	1	0.1%
505	1	0.1%
495	1	0.1%

Level 3 and 4%
Real number (ℝ_≥0)

HIGH CORRELATION

Distinct	511
Distinct (%)	57.2%
Missing	2
Missing (%)	0.2%
Infinite	0
Infinite (%)	0.0%

Mean	50.47181208
Minimum	0
Maximum	97.9
Zeros	1
Zeros (%)	0.1%
Memory size	7.1 KiB

Quantile statistics

Minimum	0
5-th percentile	14.625
Q1	35.75
median	51.25
Q3	64.45
95-th percentile	84.875
Maximum	97.9
Range	97.9
Interquartile range (IQR)	28.7

Descriptive statistics

Standard deviation	20.37568072
Coefficient of variation (CV)	0.4037041643
Kurtosis	-0.5110779366
Mean	50.47181208
Median Absolute Deviation (MAD)	14.35
Skewness	-0.06970222123
Sum	45121.8
Variance	415.1683647
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
50	14	1.6%
66.7	8	0.9%
47.1	8	0.9%
59.4	7	0.8%
54.1	6	0.7%
54.5	6	0.7%
42.9	6	0.7%
33.3	5	0.6%
27.4	5	0.6%
56.4	4	0.4%
43.9	4	0.4%
41.9	4	0.4%
53.9	4	0.4%
73.6	4	0.4%
52.1	4	0.4%
62.9	4	0.4%
55.1	4	0.4%
63	4	0.4%
48.3	4	0.4%
64.9	4	0.4%
42.7	4	0.4%
59	4	0.4%
80	4	0.4%
68.4	4	0.4%
30.3	4	0.4%
Other values (486)	765	85.4%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0	1	0.1%
0.9	1	0.1%
5	1	0.1%
6.1	1	0.1%
6.5	1	0.1%
6.9	3	0.3%
7.3	2	0.2%
7.4	1	0.1%
8.4	1	0.1%
9.2	3	0.3%

Value	Count	Frequency (%)
97.9	1	0.1%
97.7	1	0.1%
96.6	1	0.1%
95.2	1	0.1%
94.4	1	0.1%
94.3	1	0.1%
93.5	1	0.1%
93.3	1	0.1%
93.1	3	0.3%
92.9	1	0.1%

Pearson's r

The Pearson's correlation coefficient (r) is a measure of linear correlation between two variables. It's value lies between -1 and +1, -1 indicating total negative linear correlation, 0 indicating no linear correlation and 1 indicating total positive linear correlation. Furthermore, r is invariant under separate changes in location and scale of the two variables, implying that for a linear function the angle to the x-axis does not affect r.

To calculate r for two variables X and Y, one divides the covariance of X and Y by the product of their standard deviations.

Spearman's ρ

The Spearman's rank correlation coefficient (ρ) is a measure of monotonic correlation between two variables, and is therefore better in catching nonlinear monotonic correlations than Pearson's r. It's value lies between -1 and +1, -1 indicating total negative monotonic correlation, 0 indicating no monotonic correlation and 1 indicating total positive monotonic correlation.

To calculate ρ for two variables X and Y, one divides the covariance of the rank variables of X and Y by the product of their standard deviations.

Kendall's τ

Similarly to Spearman's rank correlation coefficient, the Kendall rank correlation coefficient (τ) measures ordinal association between two variables. It's value lies between -1 and +1, -1 indicating total negative correlation, 0 indicating no correlation and 1 indicating total positive correlation.

To calculate τ for two variables X and Y, one determines the number of concordant and discordant pairs of observations. τ is given by the number of concordant pairs minus the discordant pairs divided by the total number of pairs.

Phik (φk)

Phik (φk) is a new and practical correlation coefficient that works consistently between categorical, ordinal and interval variables, captures non-linear dependency and reverts to the Pearson correlation coefficient in case of a bivariate normal input distribution. There is extensive documentation available here.

First rows

	NYC Results on the New York State 2006 Math Test (Grades 3-8)	DBN	Grade	Category	Year	Mean Scale Score	Students Tested	Level 1#	Level 1%	Level 2#	Level 2%	Level 3#	Level 3%	Level 4#	Level 4%	Level 3 and 4#	Level 3 and 4%
0	NaN	07X001	3	All Students	2006	654.0	104	18.0	17.3	25.0	24.0	52.0	50.0	9.0	8.7	61.0	58.7
1	NaN	07X001	4	All Students	2006	642.0	111	25.0	22.5	40.0	36.0	41.0	36.9	5.0	4.5	46.0	41.4
2	NaN	07X001	5	All Students	2006	633.0	109	31.0	28.4	41.0	37.6	35.0	32.1	2.0	1.8	37.0	33.9
3	NaN	07X001	All Grades	All Students	2006	NaN	324	74.0	22.8	106.0	32.7	128.0	39.5	16.0	4.9	144.0	44.4
4	NaN	07X005	3	All Students	2006	661.0	96	12.0	12.5	20.0	20.8	51.0	53.1	13.0	13.5	64.0	66.7
5	NaN	07X005	4	All Students	2006	664.0	84	9.0	10.7	13.0	15.5	55.0	65.5	7.0	8.3	62.0	73.8
6	NaN	07X005	5	All Students	2006	639.0	113	25.0	22.1	41.0	36.3	43.0	38.1	4.0	3.5	47.0	41.6
7	NaN	07X005	All Grades	All Students	2006	NaN	293	46.0	15.7	74.0	25.3	149.0	50.9	24.0	8.2	173.0	59.0
8	NaN	07X018	3	All Students	2006	656.0	86	12.0	14.0	21.0	24.4	47.0	54.7	6.0	7.0	53.0	61.6
9	NaN	07X018	4	All Students	2006	655.0	72	7.0	9.7	17.0	23.6	44.0	61.1	4.0	5.6	48.0	66.7

Last rows

	NYC Results on the New York State 2006 Math Test (Grades 3-8)	DBN	Grade	Category	Year	Mean Scale Score	Students Tested	Level 1#	Level 1%	Level 2#	Level 2%	Level 3#	Level 3%	Level 4#	Level 4%	Level 3 and 4#	Level 3 and 4%
886	NaN	12X318	7	All Students	2006	621.0	184	55.0	29.9	91.0	49.5	38.0	20.7	0.0	0.0	38.0	20.7
887	NaN	12X318	8	All Students	2006	628.0	212	55.0	25.9	105.0	49.5	51.0	24.1	1.0	0.5	52.0	24.5
888	NaN	12X318	All Grades	All Students	2006	NaN	396	110.0	27.8	196.0	49.5	89.0	22.5	1.0	0.3	90.0	22.7
889	NaN	12X341	6	All Students	2006	646.0	83	11.0	13.3	33.0	39.8	38.0	45.8	1.0	1.2	39.0	47.0
890	NaN	12X341	7	All Students	2006	638.0	72	11.0	15.3	39.0	54.2	20.0	27.8	2.0	2.8	22.0	30.6
891	NaN	12X341	All Grades	All Students	2006	NaN	155	22.0	14.2	72.0	46.5	58.0	37.4	3.0	1.9	61.0	39.4
892	NaN	12X691	3	All Students	2006	666.0	16	1.0	6.3	3.0	18.8	9.0	56.3	3.0	18.8	12.0	75.0
893	NaN	12X691	4	All Students	2006	649.0	19	2.0	10.5	10.0	52.6	5.0	26.3	2.0	10.5	7.0	36.8
894	NaN	12X691	5	All Students	2006	637.0	16	3.0	18.8	8.0	50.0	5.0	31.3	0.0	0.0	5.0	31.3
895	NaN	12X691	All Grades	All Students	2006	NaN	51	6.0	11.8	21.0	41.2	19.0	37.3	5.0	9.8	24.0	47.1

Overview

Variables

Most occurring characters

Most occurring categories

Most frequent Decimal Number characters

Most frequent Uppercase Letter characters

Most occurring scripts

Most frequent Common characters

Most frequent Latin characters

Most occurring blocks

Most frequent ASCII characters

Most occurring characters

Most occurring categories

Most frequent Decimal Number characters

Most frequent Uppercase Letter characters

Most frequent Lowercase Letter characters

Most frequent Space Separator characters

Most occurring scripts

Most frequent Common characters

Most frequent Latin characters

Most occurring blocks

Most frequent ASCII characters

Most occurring characters

Most occurring categories

Most frequent Uppercase Letter characters

Most frequent Lowercase Letter characters

Most frequent Space Separator characters

Most occurring scripts

Most frequent Latin characters

Most frequent Common characters

Most occurring blocks

Most frequent ASCII characters

Most occurring characters

Most occurring categories

Most frequent Decimal Number characters

Most occurring scripts

Most frequent Common characters

Most occurring blocks

Most frequent ASCII characters

Interactions

Correlations

Pearson's r

Spearman's ρ

Kendall's τ

Phik (φk)

Missing values

Sample

First rows

Last rows